Recency bias is a useful inductive prior for sequential modeling: it emphasizes nearby observations and can still allow longer-range dependencies. Standard Transformer attention lacks this property, relying on all-to-all interactions that overlook the causal and often local structure of temporal data. We propose a simple mechanism to introduce recency bias by reweighting attention scores with a smooth heavy-tailed decay. This adjustment strengthens local temporal dependencies without sacrificing the flexibility to capture broader and data-specific correlations. We show that recency-biased attention consistently improves sequential modeling, aligning Transformer more closely with the read, ignore, and write operations of RNNs. Finally, we demonstrate that our approach achieves competitive and often superior performance on challenging time-series forecasting benchmarks.